Integrable Discrete Equations Related to the Extended Discrete KP Hierarchy

Abstract:
We investigate self-similar solutions of the extended discrete KP hierarchy. It is shown that suitable ansatzes lead to purely discrete equations with dependence on some number parameters together with equations governing deformations with respect to these parameters. Some examples are provided. In particular, we show discrete equations which describe B\"acklund transformations of Veselov-Shabat dressing chains known also as Noumi-Yamada systems of type $A_{2(n-1)}^{(1)}}$.